Fast-forwarding molecular ground state preparation with optimal control on analog quantum simulators

Abstract: We show that optimal control of the electron dynamics is able to prepare molecular ground states, within chemical accuracy, with evolution times approaching the bounds imposed by quantum mechanics. We propose a specific parameterization of the molecular evolution only in terms of interaction already present in the molecular Hamiltonian. Thus, the proposed method solely utilizes quantum simulation routines, retaining their favourable scalings. Due to the intimate relationships between variational quantum algorithms and optimal control we compare, when possible, our results with state-of-the-art methods in literature. We found that the number of parameters needed to reach chemical accuracy and algorithmic scaling are in line with compact adaptive strategies to build variational ansatze. The algorithm, which is also suitable for quantum simulators, is implemented emulating a digital quantum processor (up to 16 qubits) and tested on different molecules and geometries spanning different degrees of electron correlation.